Moduli of unramified irregular singular parabolic connections on a smooth projective curve

In this paper we construct a coarse moduli scheme of stable unramified irregular singular parabolic connections on a smooth projective curve and prove that the constructed moduli space is smooth and has a symplectic structure. Moreover we will construct the moduli space of generalized monodromy data coming from topological monodromies, formal monodromies, links and Stokes data associated to the generic irregular connections. We will prove that for a generic choice of generalized local exponents, the generalized Riemann-Hilbert correspondence from the moduli space of the connections to the moduli space of the associated generalized monodromy data gives an analytic isomorphism. This shows that differential systems arising from (generalized) isomonodromic deformations of corresponding unramified irregular singular parabolic connections admit geometric Painlev\'e property as in the regular singular cases proved generally in [8].Comment: 40 pages, 2 figure

Moduli of Stable Parabolic Connections, Riemann-Hilbert correspondence and Geometry of Painlev\'{e} equation of type VI, Part I

In this paper, we will give a complete geometric background for the geometry of Painlev\'e $VI$ and Garnier equations. By geometric invariant theory, we will construct a smooth coarse moduli space M_n^{\balpha}(\bt, \blambda, L) of stable parabolic connection on \BP^1 with logarithmic poles at D(\bt) = t_1 + ... + t_n as well as its natural compactification. Moreover the moduli space \cR(\cP_{n, \bt})_{\ba} of Jordan equivalence classes of SL_2(\C)-representations of the fundamental group \pi_1(\BP^1 \setminus D(\bt),\ast) are defined as the categorical quotient. We define the Riemann-Hilbert correspondence \RH: M_n^{\balpha}(\bt, \blambda, L) \lra \cR(\cP_{n, \bt})_{\ba} and prove that \RH is a bimeromorphic proper surjective analytic map. Painlev\'e and Garnier equations can be derived from the isomonodromic flows and Painlev\'e property of these equations are easily derived from the properties of \RH. We also prove that the smooth parts of both moduli spaces have natural symplectic structures and \RH is a symplectic resolution of singularities of \cR(\cP_{n, \bt})_{\ba}, from which one can give geometric backgrounds for other interesting phenomena, like Hamiltonian structures, B\"acklund transformations, special solutions of these equations.Comment: 76 pages, 4 figure

B\"acklund Transformations of the Sixth Painlev\'e Equation in Terms of Riemann-Hilbert Correspondence

It is well known that the sixth Painlev\'e equation \PVI admits a group of B\"acklund transformations which is isomorphic to the affine Weyl group of type $\mathrm{D}_4^{(1)}$. Although various aspects of this unexpectedly large symmetry have been discussed by many authors, there still remains a basic problem yet to be considered, that is, the problem of characterizing the B\"acklund transformations in terms of Riemann-Hilbert correspondence. In this direction, we show that the B\"acklund transformations are just the pull-back of very simple transformations on the moduli of monodromy representations by the Riemann-Hilbert correspondence. This result gives a natural and clear picture of the B\"acklund transformations. Key words: B\"acklund transformation, the sixth Painlev\'e equation, Riemann-Hilbert correspondence, isomonodromic deformation, affine Weyl group of type $\mathrm{D}_4^{(1)}$.Comment: 24pages, 4 figures, 3 eps file

Clustering Properties of Low-Luminosity Star-Forming galaxies at z = 0.24 and 0.40 in the Subaru Deep Field

We present our analysis on the clustering properties of star-forming galaxies selected by narrow-band excesses in the Subaru Deep Field. Specifically we focus on Halpha emitting galaxies at z = 0.24 and z = 0.40 in the same field, to investigate possible evolutionary signatures of clustering properties of star-forming galaxies. Based on the analysis on 228 Halpha emitting galaxies with 39.8 < log L(Halpha) < 40.8 at z = 0.40, we find that their two-point correlation function is estimated as xi = (r/1.62^{+0.64}_{-0.50} Mpc)^{-1.84 +/- 0.08}. This is similar to that of Halpha emitting galaxies in the same Halpha luminosity range at z = 0.24, xi = (r/1.88^{+0.60}_{-0.49} Mpc)^{-1.89 +/- 0.07}. These correlation lengths are smaller than those for the brighter galaxy sample studied by Meneux et al. (2006) in the same redshift range. The evolution of correlation length between z = 0.24 and z = 0.40 is interpreted by the gravitational growth of the dark matter halos.Comment: 16 pages, 7 figures, PASJ, Vol.60, No.6, in pres

Electronic Structures of N-doped Graphene with Native Point Defects

Nitrogen doping in graphene has important implications in graphene-based devices and catalysts. We have performed the density functional theory calculations to study the electronic structures of N-doped graphene with vacancies and Stone-Wales defect. Our results show that monovacancies in graphene act as hole dopants and that two substitutional N dopants are needed to compensate for the hole introduced by a monovacancy. On the other hand, divacancy does not produce any free carriers. Interestingly, a single N dopant at divacancy acts as an acceptor rather than a donor. The interference between native point defect and N dopant strongly modifies the role of N doping regarding the free carrier production in the bulk pi bands. For some of the defects and N dopant-defect complexes, localized defect pi states are partially occupied. Discussion on the possibility of spin polarization in such cases is given. We also present qualitative arguments on the electronic structures based on the local bond picture. We have analyzed the 1s-related x-ray photoemission and adsorption spectroscopy spectra of N dopants at vacancies and Stone-Wales defect in connection with the experimental ones. We also discuss characteristic scanning tunneling microscope (STM) images originating from the electronic and structural modifications by the N dopant-defect complexes. STM imaging for small negative bias voltage will provide important information about possible active sites for oxygen reduction reaction.Comment: 40 pages, 2 tables, 16 figures. The analysis of Clar sextets is added. This version is published on PHYSICAL REVIEW B 87, 165401(2013

Neural population representation hypothesis of visual flow and its illusory after effect in the brain: psychophysics, neurophysiology and computational approaches

The neural representation of motion aftereffects induced by various visual flows (translational, rotational, motion-in-depth, and translational transparent flows) was studied under the hypothesis that the imbalances in discharge activities would occur in favor in the direction opposite to the adapting stimulation in the monkey MST cells (cells in the medial superior temporal area) which can discriminate the mode (i.e., translational, rotational, or motion-in-depth) of the given flow. In single-unit recording experiments conducted on anaesthetized monkeys, we found that the rate of spontaneous discharge and the sensitivity to a test stimulus moving in the preferred direction decreased after receiving an adapting stimulation moving in the preferred direction, whereas they increased after receiving an adapting stimulation moving in the null direction. To consistently explain the bidirectional perception of a transparent visual flow and its unidirectional motion aftereffect by the same hypothesis, we need to assume the existence of two subtypes of MST D cells which show directionally selective responses to a translational flow: component cells and integration cells. Our physiological investigation revealed that the MST D cells could be divided into two types: one responded to a transparent flow by two peaks at the instances when the direction of one of the component flow matched the preferred direction of the cell, and the other responded by a single peak at the instance when the direction of the integrated motion matched the preferred direction. In psychophysical experiments on human subjects, we found evidence for the existence of component and integration representations in the human brain. To explain the different motion perceptions, i.e., two transparent flows during presentation of the flows and a single flow in the opposite direction to the integrated flows after stopping the flow stimuli, we suggest that the pattern-discrimination system can select the motion representation that is consistent with the perception of the pattern from two motion representations. We discuss the computational aspects related to the integration of component motion fields

Neural regulation in tooth regeneration of Ambystoma mexicanum

The presence of nerves is an important factor in successful organ regeneration in amphibians. The Mexican salamander, Ambystoma mexicanum, is able to regenerate limbs, tail, and gills when nerves are present. However, the nerve-dependency of tooth regeneration has not been evaluated. Here, we reevaluated tooth regeneration processes in axolotls using a three-dimensional reconstitution method called CoMBI and found that tooth regeneration is nerve-dependent although the dentary bone is independent of nerve presence. The induction and invagination of the dental lamina were delayed by denervation. Exogenous Fgf2, Fgf8, and Bmp7 expression could induce tooth placodes even in the denervated mandible. Our results suggest that the role of nerves is conserved and that Fgf+Bmp signals play key roles in axolotl organ-level regeneration. The presence of nerves is an important factor in successful organ regeneration in amphibians. The Mexican salamander, Ambystoma mexicanum, is able to regenerate limbs, tail, and gills when nerves are present. However, the nervedependency of tooth regeneration has not been evaluated. Here, we reevaluated tooth regeneration processes in axolotls using a three-dimensional reconstitution method called CoMBI and found that tooth regeneration is nerve-dependent although the dentary bone is independent of nerve presence. The induction and invagination of the dental lamina were delayed by denervation. Exogenous Fgf2, Fgf8, and Bmp7 expression could induce tooth placodes even in the denervated mandible. Our results suggest that the role of nerves is conserved and that Fgf+Bmp signals play key roles in axolotl organ-level regeneration